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Estimation of tail thickness parameters from GJR-GARCH models

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  • Iglesias, Emma M.
  • Linton, Oliver

Abstract

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes and extends the method proposed by Berkes, Horváth and Kokoszka (2003). We show that the estimator of tail thickness is consistent and converges at rate √T to a normal distribution (where T is the sample size), provided the model for conditional variance is correctly specified as a GJR-GARCH. This is much faster than the convergence rate of the Hill estimator, since that procedure only uses a vanishing fraction of the sample. We also develop new specification tests based on this method and propose new alternative estimates of unconditional value at risk. We show in Monte Carlo simulations the advantages of our procedure in finite samples; and finally an application concludes the paper

Suggested Citation

  • Iglesias, Emma M. & Linton, Oliver, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," UC3M Working papers. Economics we094726, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we094726
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    Cited by:

    1. Iglesias, Emma M., 2015. "Value at Risk of the main stock market indexes in the European Union (2000–2012)," Journal of Policy Modeling, Elsevier, vol. 37(1), pages 1-13.
    2. Ngai Chan & Liang Peng & Rongmao Zhang, 2012. "Interval estimation of the tail index of a GARCH(1,1) model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 546-565, September.
    3. Emma M. Iglesias, 2012. "An analysis of extreme movements of exchange rates of the main currencies traded in the Foreign Exchange market," Applied Economics, Taylor & Francis Journals, vol. 44(35), pages 4631-4637, December.
    4. Degiannakis, Stavros & Floros, Christos & Livada, Alexandra, 2012. "Evaluating Value-at-Risk Models before and after the Financial Crisis of 2008: International Evidence," MPRA Paper 80463, University Library of Munich, Germany.
    5. Emma M. Iglesias & Mar�a Dolores Lagoa Varela, 2012. "Extreme movements of the main stocks traded in the Eurozone: an analysis by sectors in the 2000's decade," Applied Financial Economics, Taylor & Francis Journals, vol. 22(24), pages 2085-2100, December.
    6. Beran, Jan & Schell, Dieter, 2012. "On robust tail index estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3430-3443.
    7. Iglesias, Emma M., 2015. "Value at Risk and expected shortfall of firms in the main European Union stock market indexes: A detailed analysis by economic sectors and geographical situation," Economic Modelling, Elsevier, vol. 50(C), pages 1-8.

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    More about this item

    Keywords

    Pareto tail thickness parameter;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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